Flight is one of the biggest bang for the tech buck advances. You get an economic advance, a major mobility advance, and a powerful military advance, all in one technology. There are few other techs which give so much in one go.
But there are a few others -- construction, assembly line, railroad, for example -- which revolutionize how your empire performs. But Flight is one of the best of these, possibly the best.
Its effect is most pronounced on a map with many separate land masses or islands, and with an empire spread across them. Once you get Flight, your transports can practically retire, except as military invasion craft, as airlifts move the majority of your units around. The task of delivering missionaries, executives, and spies, which is tied to slow transports, suddenly becomes a matter of instant mobility, no delays (except to let the spies reach their final destination).
If you are using spies frequently, one of the biggest downsides is the turnaround time after a mission. Being able to teleport back to a frontier (or vassal) city saves a huge amount of time.
So even ignoring the military aspects, the airlifts alone are a big boon for any widespread civilization. Being able to deliver military units to defend any city, you are much better prepared to defend.
Assuming flight along with assembly line, your cities can be quite productive. Radio isn't that much farther along, so if you've waited for an advantage to begin warring, Flight definitely qualifies as a significant advantage. Using fighters plus airlifts to speed up your first war, then bombers to continue the process, you can truly pull off blitzkrieg wars.
Without Flight, it is much harder to do except against a weaker enemy. Flight lets you leverage the attack against an enemy who is roughly comparable to you in every other way. If key enemy resources are within air range, you can open a war by denying them access to key resources like oil and coal. Take those two resources out, and most enemies simply won't be able to replace losses effectively.
Much depends on playing style, but if you either felt like peaceful expansion for its own sake, or because you didn't think you had enough of an edge to conquer, Flight can trigger a change in aggression.
Too bad the AI doesn't quite feel that way about it. They do use it, and spies, to reduce your resources but I don't think they are quite as aggressive as a human can be.
Railroad is my next pick for a super-tech. Faster movement, always useful and it definitely changes how you manage your empire. Production boosts, never hurt and again a big gain. A nice defender, while not good for aggressive wars machine guns can negate a lot of threats cheaply. But the biggest effect is the Mining Inc corporation. Get it and exploit it, and even your small cities are productive, as well as moneymakers for your empire. While railroad doesn't give you an immediate tag-team powerup for war, it gets you ready for whichever warlike tech you do use (like Rifling).